Advertisements
Advertisements
प्रश्न
Find the derivative of x2 cosx.
उत्तर
Let y = x2 cosx
Differentiating both sides with respect to x, we
`(dy)/(dx) = d/(dx)(x^2 cos x)`
= `x^2 d/(dx) (cos x) + cos x d/(dx) (x^2)`
= `x^2(- sinx) + cosx (2x)`
= `2x cosx - x^2 sinx`
APPEARS IN
संबंधित प्रश्न
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
(x + a)
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
(ax + b)n
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(sin(x + a))/ cos x`
\[\frac{1}{\sqrt{x}}\]
\[\frac{x^2 + 1}{x}\]
(x + 2)3
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
\[\sin \sqrt{2x}\]
x4 − 2 sin x + 3 cos x
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
sin x cos x
x5 ex + x6 log x
(x sin x + cos x ) (ex + x2 log x)
(1 − 2 tan x) (5 + 4 sin x)
x3 ex cos x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
(ax + b)n (cx + d)n
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
